Sadie makes excellent points about looking for formal written loan approval - this will give you the real number a bank will lend to you, along with the terms and conditions of the offer (how much deposit they want you to have, and how many years to pay for example)
The written loan approval means the bank will lend to you, subject to no substantial change in your circumstances when it comes time to buy your new house, so it takes some uncertainty out of the whole situation for you.
There is a vital caveat though - if any of the circumstances on the original loan application you submit have changed, the bank will not be obliged to offer the loan - this includes the situation where you've changed your mind about the house you want to buy, and have found a new one - a fairly frequent occurrence.